The Volts left the field last night requiring 153 runs to win with eight wickets in hand.
A brilliant spell of bowling and a spectacular middle-order collapse sent the home side into bat after Wellington was dismissed for 309 in its second innings late yesterday afternoon.
Wellington resumed at 107 for one yesterday morning and went about its work well, adding 56 runs before Stephen Murdoch was bowled by Jimmy Neesham.
Wellington opener Michael Papps continued to anchor his side's innings and he and Michael Bracewell added another 80 runs before the former Otago player was lbw to Anaru Kitchen.
Papps added another century to his impressive domestic record and put his side in a good position at 270 for three.
Papps was eventually out after Michael Rae tempted him with a half-track delivery the batsman attempted to pull square of the wicket.
Michael Rippon took a boundary-riding catch and that signalled the beginning of the end for Wellington.
Two overs later Rae struck again, trapping Fraser Colson in front and, three balls later, Rae bowled Logan van Beek with an almost identical ball to leave the visiting side reeling.
Jacob Duffy dismissed Devon Conway lbw with his first ball of the next over before new batsman Jeetan Patel edged his second ball to Mark Craig at second slip as Wellington lost three wickets in three balls.
Rae, 12th man until team-mate Shaun Hicks was ruled out of the match after suffering a blow to the helmet when fielding in close on the second day, quickly dismissed Ian McPeake and Hamish Bennett to finish with five for 18.
The fast fall of Wellington wickets gave a huge boost to Otago which went out to bat requiring 215 to win.
Openers Rob Nicol and Hamish Rutherford set about chasing that down late yesterday afternoon.
Otago suffered an early setback when Rutherford was gone just four runs into his side's chase.
Nicol and new first drop Rippon played cautious cricket, attempting to see out the day's play.
They were successful in getting through 20 overs of play before Rippon was out lbw off McPeake's bowling.
That brought Kitchen to the crease. He played his shots and hit three fours before the close of play to get to 17 not out.
Nicol left the field on 27 from 93 balls.
